How do I stop my texture from stretching when I pose my character?
In real the material on the knee would be either

compressed when the knee is straight and normal when it is bent ... or ...
normal when the knee is straight and stretched when the knee is bent.

If you want to &quot;float&quot; it out of thin air, you need to hide some extra geometry below the surface, like pi75 mentioned in the comment above.
Proof of concept